When Does the Decade End?

I have seen this question asked (or its fraternal twin, “when does the new decade begin”) in a number of places, and my response is this:

That’s a lousy way to phrase the question.


I will remind folks that I work at the Naval Observatory, but this blog in no way represents the official position of USNO. That said, I am one of the people who might be consulted on such a question, if it were difficult to figure out. But it wouldn’t get that far. This is not a “math is hard” subject.

The question is ambiguous, which is why it’s a lousy way to ask it. There is no “the decade” because there are a number of ways to label decades. A decade is a period of 10 years. 2010-2019 is a decade (we would call that the 2010s), as is 2011-2020 (the 202nd decade). The latter is based on numbering the decades, as we tend to do with centuries and millennia, which started with the year 1. The former is a count of an interval, which is a perfectly cromulent way to keep track of things —if we have a meeting on Wednesday and we say “see you in a week” we start counting from that point, not from Sunday (the equivalent of starting at 1). We can use time labels as an interval. We do it all the time. Almost nobody gets confused by this.

Which means the immediate response to the question in the title should be “to which decade are you referring?”  Without that clarification, you get the mess that I’ve been seeing. People assuming one protocol, and, what’s worse, denying that there is another. Instead they blindly point to an authority they claim will back them up, citing the Naval Observatory and the Farmer’s Almanac, except…

The few people who have provided a link sent me to discussions of when the 2nd millennium/20th century ended; some are leftover from these discussions from 20 years ago. Nothing about decades. No discussion of intervals, because when the 2nd millennium/20th century ended has already defined the discussion in a way that “the decade” has not.

The Farmer’s Almanac citation may be from this NPR piece

We ran a story several years ago. In fact, you know, remember the big celebration in 1999. People thought that the new millennial (sic) was going to start the next year. But really, a decade begins actually with the year ending in the numeral one. There was never a year zero. So when we started counting time way back when, it goes one through 10. So a decade is 10 years.

See the problem? It starts with the millennium discussion and applies it. That last sentence — a decade is 10 years — is true and has nothing to do with the bit that preceded it. The fact that there was no year zero has nothing to do with using decade as an interval of time.

NPR does better here

…the definition of a decade is just any 10-year span. Where it begins is fairly arbitrary, in their view.

Rick Fienberg of the American Astronomical Society says he doesn’t think his group has adopted an official position on the matter — but he adds, “History is clear: Because there was no Year Zero, the first decade of the common era (CE or AD) was years 1 to 10, the second decade was years 11 to 20, and the next decade will be years 2021 to 2030.”

Part of the issue, he and others say, is our use of “decade” as a frame of cultural reference.

“The reason people get confused is because we tend to think of decades as ‘the 20s’ or ‘the 30s,’ Fienberg says. “It’s true that ‘the 20s’ — that is, the period 2020 to 2029 — is a decade, i.e., 10 years

Fienberg lays out both cases for you.

The biggest mistake in all of this is people saying that the teens (2010s) don’t end for another year. They have taken both conventions and mashed them together into a horrible, horrible mess. You can talk about the 2010s decade, which ends (as I write this) tonight, and you can talk about the 2nd decade of the third millennium (or any similar numbering convention) which started in 2011 and doesn’t end for another year.

If the US founding fathers had settled on 5-year terms for presidents, it’s quite likely that we in the US would be referring to presidential decades for two-term presidents. Since Washington was sworn in in 1789, we would have these decades for two-termers starting on 9s and 4s (since not all presidents served two terms). And maybe there would be slightly less confusion about such a relatively simple concept.


Pick one convention or the other, as appropriate, and be consistent. Recognize that the other convention exists. And ask better questions.


A Hard Day's Night

Correction: Tonight will not be the longest night in the history of Earth

The article below said that, due to the rotation of the Earth gradually slowing down over time, this winter solstice would feature the longest night ever.

I got this wrong. The Earth’s rotation is gradually slowing on an extremely long timescale, but on a shorter year-to-year basis, geologic factors can alter the speed as well.

Right basic idea— the rotation rate is slowing as a long-term trend — but wrong execution.

Are You High, Noon?

High Noon

If we consider “noon” to be the time at which the sun is highest in the sky then the time between successive noons is not quite 24 hours. Relative to our clock, our sundial will seem to run a bit fast on some days, and a bit slow on others. Because of this, if we note the position of the Sun at clock noon over the course of a year, it will mark out a figure-8 pattern known as an analemma.

Don't Forget to Put a Stitch in it

How Time Is Made

Here’s another timing article that popped up right after Daylight Saving Time ended. (Perhaps a heavy sigh is required here. I’m not sure why the rash of stories has hit is) I’m predisposed to like it, since it’s largely focused on our work, but unlike some articles I’ve critiqued lately, it doesn’t focus on one US timekeeping group and ignore the other one

By law, today the USNO shares the responsibilities for measuring and disseminating time with the Time and Frequency department of the National Institute of Standards and Technology (NIST), which sits under the US Dept. of Commerce. The USNO sets time for GPS and navigational systems and the Dept. of Defense, while NIST sets the standard for the financial sector and other civilian applications. (NIST receives several billion computer requests per day for this service, and broadcasts time to over 50 million radio clocks, wristwatches, and other clocks with radio receivers.) While there is a lively cooperation between the two agencies charged with telling the time—and the occasional competition over talented PhDs—they mostly operate in different domains: NIST performs most of the cutting-edge research, while USNO focuses on counting and disseminating the time to the military, as a matter of national security.

I don’t even object to the observation that NIST is doing most of the cutting-edge research — they are. Their frequency standard results are amazing. Our research in that area is different, since it focuses on developing continuously-running clocks.

You Keep Using That Word…

It’s time for another installment of “That’s Not A Clock (it’s a stopwatch)”

New Clock May End Time As We Know It. This is the same technology that I’d linked to back in January, and NPR did something back then, too. I thought maybe this was prompted by a new paper, but the story may have just been motivated by our daylight saving shift last weekend.

I completely agree with Tom O’Brian — time is a human construct, in that it’s abstraction we came up with (but then, so is length). But I have an issue with saying that NIST has America’s master clock, while ignoring the one that resides in Washington DC, run by the navy, and that Tom O’Brian is America’s official timekeeper (i.e. singular). Sins of omission.

This new clock can keep perfect time for 5 billion years.

…if it ran continuously. But it doesn’t. Jun Ye gave a talk on this at DAMOP this past summer, and someone asked him if/when any of these optical lattice devices were going to run as actual clocks, and how long they could run. The answer was (paraphrasing here) “about 24 hours, because people need to sleep.” NIST isn’t going to be pushing very hard to extend that, because that’s not their job. As he put it, once you get to the noise limit of the device, they sort of lose interest in running it any longer.

The rest of it is pretty good for a pop-sci piece, aside from the observation that (as Matthew Francis tweeted at me) “end time as we know it” seems a trifle hyperbolic. In other words, what do you mean, “we”? The issues of trying to synchronize clocks are not going to affect the vast majority of people. It’s a very interesting technical challenge, for reasons described in the article, and once people come up with applications that require picosecond-ish level of timing or better, it’s something we’ll have to solve. But it’s not going to affect whether you’re late for work or what time the game comes on.

Déjà Vu All Over Again

The man who keeps America on time

Reminiscent of yesterday’s video — our chief scientist saying similar things, mostly as a proxy for the efforts of my hard-working colleagues (and me). You get a nice view of our wonderful library, though our wonderful librarians are out of view.

I should point out that when Chris Wallace talks about cesium clocks, what the camera is pointing to (that big black box) is a hydrogen maser. Shhh. That’ll be our little secret.

There’s a bonus! An ad at the beginning. The kind you’d expect at Fox news. Sorry.

Time Travel Back to Last Wednesday

How We Got to Now: Time

My travel caused me to miss the original airing of this, and the site says it’s only active until the 30th. There’s a bit on the Naval Observatory and our (my) Rubidium Fountain Clocks at somewhere around the 45-minute mark, featuring our chief scientist.

A nit/peeve (from the intro to atomic timekeeping): atomic physics and nuclear physics are separate things. Even though we call it atomic power or an atomic bomb, it’s all nuclear processes. The physics behind atomic clocks is not really tied, except at a fairly superficial level, to that of bombs.

Watch for an Infestation of Time Flies

Having Fun with the Equation of Time

For most of history, the daily passage of time was denoted by the Sun. Solar Noon occurs when the Sun stands at its highest elevation (also known as its altitude) above the local horizon when it transits the north-south meridian. The trouble is, the passage apparent solar time doesn’t exactly match what we call solar mean time, or the 24 hour rotation of the Earth. In fact, this discrepancy can add up to as much as more than 16 minutes ahead of solar noon in late October and November and over 12 minutes behind it in February. This is worth bringing up this week because this factor, known as “The Equation of Time” — think “equation” in the sense that sundial owners must factor it in to make solar mean and apparent time “equal” — reache[d] its shallow minimum for 2014 this Saturday at 7:00 UT/3:00 AM EDT with a value of -6.54 minutes.

300th Anniversary of the Longitude Act

Maritime museum finds time for celebration of Harrison’s sea clocks

The exhibition marks the 300th anniversary of the Longitude Act, passed in 1714, which established the Longitude Board and offered a vast £20,000 prize to anyone who could solve the problem of measuring longitude at sea. It includes the actual act of parliament, passed in the last weeks before the death of Queen Anne, on display for the first time.

The story of John Harrison, the carpenter and self-taught genius clockmaker who invented a series of ever more accurate clocks and then a cabbage-sized watch that solved the problem, but never got the full prize from the board, inspired Dava Sobel’s bestselling book and film, Longitude.

This is the reason why my job (making atomic clocks — real clocks) is a navy job — precise navigation requires precise time. The transition to GPS hasn’t changed that fact. Poor navigational ability is costly:

In a storm in 1707, when an entire British fleet was driven onto the rocks at Scilly believing they were safely out at sea, more than 1,400 sailors drowned.

More: Why longitude mattered in 1714

This Particular Ship Has Sailed

Greenwich Mean Time could drift to the US, minister warns

Time will become meaningless and people’s experience of night and day will change fundamentally if the world goes ahead with plans to scrap leap seconds, the science minister has warned.


Most people can’t tell the difference; GMT is solar time and currently universal coordinated time (UTC) is atomic, but is adjusted to keep in synch with the sun, because the earth’s rotation rate is a tiny bit slower than it used to be, and the broad trend is that it continues to slow. But even if these are no longer tied to each other, so what?

Without them atomic clocks, which are used as the basis of international time, would fall out of sync with the cycle of night and day. Nearly 800 years from now, the sun would reach its highest point at 1pm, rather than midday.

Right now, the sun doesn’t reach its highest point at noon for the vast majority of the population, and I’m not even worrying about all of us who experience daylight “saving” (or summer) time, where we shift our clocks forward an hour, so that this nominal noon effect actually does happen at 1 PM (without any apparent hysteria or crumbling of empires).

The sun is only overhead (or on a line going overhead) at noon if you are on the actual meridian for your time zone, and then it’s only overhead at noon on the solstices, as I have mentioned a couple of times before — the overhead sun on the meridian varies by ± 15 minutes, and most of us live elsewhere. Meaning that a) this isn’t an actual problem, and b) it will take 800 years before we reach as much skewing as we presently inflict upon ourselves.

“Going purely for an atomic clock option would lose contact with time as we experience. My view is that the relatively frequent but modest corrections are better than allowing a discrepancy to build up. Greenwich Mean Time would slowly move west towards America. I want to keep it in Britain.”

Official time (UTC) is kept by the international Bureau of Weights and measures in Paris. So this is just more hyperbole.